Elliptic curve isogeny class with Cremona label 485520fj (LMFDB label 485520.fj)

• Label: 485520fj
• Number of curves: $6$
• Conductor: $485520$
• CM: no
• Rank: $0$

Elliptic curves in class 485520fj

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
485520.fj5	485520fj1	\([0, 1, 0, -4431, -468576]\)	\(-24918016/229635\)	\(-88685290517040\)	\([2]\)	\(1310720\)	\(1.3588\)	\(\Gamma_0(N)\)-optimal^*
485520.fj4	485520fj2	\([0, 1, 0, -121476, -16293060]\)	\(32082281296/99225\)	\(613132872710400\)	\([2, 2]\)	\(2621440\)	\(1.7054\)	\(\Gamma_0(N)\)-optimal^*
485520.fj3	485520fj3	\([0, 1, 0, -173496, -1040796]\)	\(23366901604/13505625\)	\(333816786253440000\)	\([2, 2]\)	\(5242880\)	\(2.0519\)	\(\Gamma_0(N)\)-optimal^*
485520.fj1	485520fj4	\([0, 1, 0, -1942176, -1042439580]\)	\(32779037733124/315\)	\(7785814256640\)	\([2]\)	\(5242880\)	\(2.0519\)
485520.fj2	485520fj5	\([0, 1, 0, -1872816, 982525620]\)	\(14695548366242/57421875\)	\(2838578114400000000\)	\([2]\)	\(10485760\)	\(2.3985\)	\(\Gamma_0(N)\)-optimal^*
485520.fj6	485520fj6	\([0, 1, 0, 693504, -7629996]\)	\(746185003198/432360075\)	\(-21373176101186918400\)	\([2]\)	\(10485760\)	\(2.3985\)

^*optimality has not been determined rigorously for conductors over 400000. In this case the optimal curve is certainly one of the 4 curves highlighted, and conditionally curve 485520fj1.

Rank

The elliptic curves in class 485520fj have rank \(0\).

Complex multiplication

The elliptic curves in class 485520fj do not have complex multiplication.

Modular form 485520.2.a.fj

Isogeny matrix

The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the Cremona numbering.

\(\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 4 & 8 & 8 \\ 2 & 1 & 2 & 2 & 4 & 4 \\ 4 & 2 & 1 & 4 & 2 & 2 \\ 4 & 2 & 4 & 1 & 8 & 8 \\ 8 & 4 & 2 & 8 & 1 & 4 \\ 8 & 4 & 2 & 8 & 4 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.